
In Section 4 we also use the relations [1]}
\(\begin{array}{l}\frac{d}{dz}\big [z^{\mathrm {c}-1}(1-z)^{\mathrm {b}-\mathrm {c}+1}F(\mathrm {a},\mathrm {b};\mathrm {c};z)\big ]=(\mathrm {c}-1)z^{\mathrm {c}-2}(1-z)^{\mathrm {b}-\mathrm {c}}F(\mathrm {a}-1,\mathrm {b};\mathrm {c}-1;z),\vspace{8.53581pt}\\\frac{d}{dz}\big [(1-z)^{\mathrm {a}}F(\mathrm {a},\mathrm {b};\mathrm {c};z)\big ]=-\frac{\mathrm {a}(\mathrm {c}-\mathrm {b})}{\mathrm {c}}(1-z)^{\mathrm {a}-1}F(\mathrm {a}+1,\mathrm {b};\mathrm {c}+1;z),\end{array}\) 
